index of tables

Since early in the history of mathematics, tables have served to aid in various computational tasks. Even today, with the ready availability of powerful calculators, tables still serve an important pedagogical purpose. Tables are found in the main text of mathematical papers and books, to illustrate the concepts in question, and as the back matter of books.

2 Logical tables

Truth tables can be made for some fairly complicated expressions, but the ones of most use to computer programming students are those for the basic expressions, a truth table for logical AND, a truth table for logical OR, a truth table for logical XOR, etc. These can be expressed as binary operations by simply replacing TRUEs with 1s and FALSEs with 0s.

For functions with a very small range of possible output values, such as the Möbius function -2<μ⁢(n)<2 or the Liouville function|λ⁢(n)|=1, it makes sense for a table to pair them up with their matchingsummatory functions. Thus we have a table of values of the Möbius function and the Mertens function and a table of values of the Liouville function and its summatory function.

Moving on to the complex plane, just a few complex multiplication tables would be sufficient, as it would be easier for the student to learn the formula for complex multiplication rather than to try to memorize some multidimensional table which would be too large even if limited to a small range.